NCERT Class 10 Solutions: Real Numbers (Chapter 1) Exercise 1.4 –Part 2

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In the questions, below find the types of decimals.

Q.III)

Is terminating if

  • p and q are co-prime

  • q is of the form Where n and m are non-negative integers

Checking Co-prime

64 and 455 have no common factors, so, 64 and 455 are co-prime

For denominator 455

Given the factors and find the factor of 455

Given the Factors of 455

Given the factors and find the factor of 455

Hence

So, denominator is not of the form

Thus has a non-terminating repeating decimal

Q.IV)

Is terminating if

  • p and q are co-prime

  • And q is of the form Where n and m are non-negative integers

Checking Co-prime

3 and 320 have no common factors, so, 3 and 320 are co-prime

For denominator 320

Image describing the factorization of 320

Factorization of 320

Image describing the factorization of 320

Hence

So, denominator is of the form

Where

Thus i.e. is terminating decimal

Q.V)

Is terminating if

  • p and q are co-prime

  • And q is of the form Where n and m are non-negative integers

Checking Co-prime

29 and 343 have no common factors, so, 29 and 343 are co-prime

For denominator 343

Image describing the factorization of 343

Factorization of 343

Image describing the factorization of 343

Hence

So, denominator is not of the form

Thus has a non-terminating repeating decimal